Do you have to register each drone you own?

It depends on your use but, generally, no.

Q34. If I own multiple sUAS, do I have to register them all?
A. Owners who fly their sUAS only as model aircraft can use one registration number on all their aircraft. Owners who fly sUAS for purposes other than as a model aircraft must register each aircraft and mark each aircraft with its unique identifier provided when registering.

https://www.faa.gov/uas/registration/faqs/

you get a set of that you can use on as many drones as you want

For recreational flying you don't register any drones.
You register the owner and the FAA doesn't care how many you have.

Good question. Thanks for the info!

Thanks guys, I really appreciate it.